A set of quantum states can be virtually cloned if and only if their density matrices are linearly independent, and the optimal 1-to-2 cloning cost for any pair of pure states equals sqrt(1+|⟨ψ1|ψ2⟩|²).
Direct observation of any two-point quantum correlation function
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abstract
The existence of noncompatible observables in quantum theory makes a direct operational interpretation of two-point correlation functions problematic. Here we challenge such a view by explicitly constructing a measuring scheme that, independently of the input state $\rho$ and observables $A$ and $B$, performs an unbiased optimal estimation of the two-point correlation function $\operatorname{Tr}[A \ \rho \ B]$. This shows that, also in quantum theory, two-point correlation functions are as operational as any other expectation value. A very simple probabilistic implementation of our proposal is presented.
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Virtual Cloning of Quantum States
A set of quantum states can be virtually cloned if and only if their density matrices are linearly independent, and the optimal 1-to-2 cloning cost for any pair of pure states equals sqrt(1+|⟨ψ1|ψ2⟩|²).